Method and apparatus for predicting and controlling the quality of a resistance spot weld

ABSTRACT

During a weld period the weld parameters are monitored and data representing the weld resistance curve and the power curve are acquired and stored for analysis by a suitably programmed computer. The derivative of R, R is calculated and stored and the function is divided by power P to obtain R/P. The resistance curve is searched to obtain the maximum value R m  which occurs during the heating phase and the function R/P is searched prior to the time of R m  to find the maximum of that curve representing the highest rate of resistance increase. Then the R/P curve is searched subsequent to its maximum to determine when the function reaches a specified percentage of the maximum. That value occurs at the knee of the resistance curve and approximates the onset of melting in the weld. 
     A prediction of whether a weld is a nugget or a sticker is made by calculating the ratio of weld energy after the onset of melting to the total weld energy, the ratio of the resistance drop after the resistance peak to the peak resistance, and then a weighted sum of the energy ratio and resistance drop ratio. 
     An edge weld geometry is detected by calculating from the resistance and power curves the weld energy during the period of expulsion, if any, divided by the cumulative energy between the onset of melting and the end of expulsion, a measure of expulsion intensity based on the maximum degree of resistance inflection, and then a weighted sum of the energy value and the inflection value.

This invention relates to a method and apparatus for analysis of aresistance spot weld and more particularly for the prediction of weldquality and optionally controlling weld quality.

To assure the integrity of spot welded parts it is often the practice toimprove weld quality by analyzing welds as they are being made to assistin the proper set up of welding equipment, to utilize ongoing weldanalysis throughout the production of welded parts and even to use theweld analysis as a feedback control to the welding equipment foradjusting the applied weld heat or selecting the optimum weldtermination for each weld. In the design of such systems it has longbeen recognized that the weld resistance curve is a useful parameter tomonitor for determining the progress of a weld particularly the growthof a weld nugget. Typically during the weld heating phase the resistancecurve reaches a maximum and then falls off. The degree of resistancedrop has been utilized as a valuable indicator of nugget growth and as acontrol for the termination of weld. This weld analysis technique andkindred techniques have led to improvements in weld integrity ascompared with non-monitored welds. However, due to the many variablesencountered in welding conditions, a high percentage of good welds hasnot been obtained on a regular basis. To compensate for the uncertaintyof weld integrity there is a tendency to apply extra welds to a part.This is not only expensive but some parts do not lend themselves to thispractice. A given welder may encounter many variables in a singleapplication. Electrode wear or deformation is always a factor to contendwith and since a given welder may be used on different regions of agiven assembly, it may encounter different kinds of metals, metals withor without zinc coatings, different stack up thicknesses and differentnumbers of sheets to be welded, for example. The previously knownanalysis techniques were not adequate to contend with the many variableconditions.

It has been found that there are weld parameters which when properlyinterpreted are capable of predicting when a sound weld nugget has beenformed even though the welding conditions and the welded parts varygreatly from one weld gun to another or within a series of welds for agiven weld gun. Development of this prediction capability has shown thatresistance spot welds can be monitored to accumulate quality controldata and that individual welds can be controlled according to qualitypredictions.

It is therefore, an object of this invention to provide a method andapparatus to predict the quality of a resistance spot weld for thepurposes of quality control as well as for weld control.

The invention is carried out by measuring the weld resistance and powerduring the formation of a resistance spot weld, determining from thoseparameters the onset of melting of the weld nugget, determining from themeasured power the total energy put into the weld and the energy putinto the weld after the onset of melting, and assessing the degree ofweld growth by comparing the ratio of the two determined energy valuesto an empirical standard ratio.

The method of the invention also comprehends the additional step ofdetermining the resistance peak and the resistance drop following thepeak, calculating the ratio of the resistance drop to the resistancepeak, and assessing the weld growth by a weighted sum of the resistanceratio and the energy ratio.

The method of the invention also optionally includes the step ofcontrolling weld quality by terminating the weld current when the abovemethod indicates a good weld has been made.

The invention is also carried out by weld monitoring apparatus havingsensors for acquiring resistance and power data during the weldformations, and a digital computer for storing the information, thecomputer being programmed to perform the above methods.

The above and other advantages of the invention will become moreapparent from the following description along with the accompanyingdrawings wherein:

FIG. 1 is a graph of a typical weld resistance curve,

FIG. 2 is a diagram of a welding system with weld monitoring apparatusaccording to the invention,

FIG. 3 is a flow chart of software procedures used for weld monitoring,

FIG. 4 is a graph of effective thermal capacitance of the weld volumevs. temperature,

FIGS. 5a and 5b are idealized curves for weld resistance and rate ofresistance change,

FIGS. 6a and 6b are representative curves for weld resistance and rateof resistance change,

FIG. 7 is a weld resistance curve illustrating the effect of highinitial contact resistance,

FIG. 8 is a weld resistance curve illustrating the effect of cool timeinterruption,

FIG. 9 is a flow chart of a computer program for detecting the onset ofmelting,

FIG. 10 is a weld resistance curve illustrating the R drop determinationfor multipulse welds,

FIG. 11 is a flow chart of a computer program for making anugget/sticker prediction,

FIGS. 12a, 12b and 12c are electrode placement diagrams showing interiorand edge weld geometries,

FIGS. 13a, 13b and 13c are typical weld resistance (R), R and R curvesrespectively for interior welds,

FIGS. 14a, 14b and 14c are typical weld resistance (R), R and R curvesrespectively for edge welds, and

FIG. 15 is a flow chart of a computer program for making aninterior/edge weld prediction.

The Input Variables

The fundamental concept underlying the analysis technique is that thegrowth of a weld may be tracked with considerable consistency byobserving the time histories of the electrical resistance R(t) of theweld, the electrical power P(t) put into the weld, and the cumulativeheating energy E(t). FIG. 1 shows a typical R-curve and the aspects ofthe weld growth which can be monitored from the curve.

Though resistance, power and energy cannot be measured directly, theyare derived from the tip voltage v(t) and primary current i(t) which aresensed directly. The preferred procedure for calculating the resistancefrom continuously sampled measurements on voltage and current is thefollowing least-means-squares approach. The welder circuit is modeled asa series inductance and resistance, and the voltage is thereforeexpressed as:

    v=Ri+L di/dt+C

where

v=voltage

i=current

di/dt=current rate of change

R=resistance

L=inductance

C=combination of voltage and

current sensor offsets

The average value of resistance is computed at each half cycle byperforming a least-mean-square regression analysis of i onto v in theabove equation. The input values for v and i are obtained by theperiodic sampling of the voltage and current sensors, and di/dt iscomputed by time differencing the current samples. The regressionanalysis produces values for R, L and C at each half cycle.

The power is given by:

    P(t)=R(t) i.sup.2 (t)

and the cumulative energy is given by: ##EQU1##

To assess weld quality it is first desired to determine whether a weldis a "nugget" or a "sticker". A nugget is a sound weld wherein two ormore sheets are thoroughly fused together, and a sticker is a weak weldhaving a superficial or surfacing joining. A nugget/sticker model isused to distinguish between the two welds. Input values to the systemare the weld resistance curve and power curve, or voltage and currentdata from which the curves are computed. A key feature to be identifiedis the knee of the resistance curve which roughly corresponds to theonset of melting, or the beginning of nugget formation. Thenugget/sticker model uses the ratio of weld energy after the onset ofmelting to total weld energy as the primary nugget/sticker discriminant,although the percentage resistance drop from the resistance peak is alsoutilized. Some of the welds thus identified as nuggets may occur at theedge of a sheet and are undesirable because of insufficient strength orbecause of aesthetic considerations. An interior/edge model is used todiscriminate between these conditions. The resistance curve is analyzedto determine whether expulsion of molten metal from the weld occurs. Ifnot, the weld is interior. If there is expulsion, the resistance curvereveals when the expulsion occurs and its intensity. The ratio of weldenergy during expulsion to weld energy between the onset of melting andthe end of expulsion is a primary edge weld indicator although theexpulsion intensity is also significant.

Apparatus

FIG. 2 shows apparatus to monitor and/or control a spot welder 10. Acontroller 12 coupled to the welder by a transformer 14 supplies weldcurrent and voltage to steel sheets 16 being welded. Voltage and currentsensors 18 and 20 respectively produce analog signals proportional tothe welder voltage and current. It is preferred that the voltage sensorleads be placed as close as possible to the welder electrodes (toeliminate the measurement of voltage due to distributed resistance inthe gun arm and secondary cables); however, this is not a requirementfor satisfactory operation of the monitor/controller. The current sensormay be placed anywhere in either the primary, or secondary circuits ofthe welder.

Due to the complexity of the computational procedures required tocalculate the quality assessment, the welder control signal, and edgediscrimination, it is preferred that the monitoring/control apparatus beimplemented with digital computation equipment, although alternativecomputation means may be used to perform the same procedures.Analog-to-digital conversion means 22 sample the voltage and currentsignals and convert the signals to discrete time waveforms which arestored in the system memory 24. The computational equipment 26 operateson the waveform data to produce the quality and edge assessments, whichmay be displayed at readout device 28 and/or transmitted to supervisorysystems (not shown) and the welder shut-off control signal which istransmitted to the welder control logic via feedback line 30. A DigitalEquipment Corporation VAX 11/780 computer with the VMS 3.0 operatingsystem is used to carry out the computations. The computer is programmedaccording to the program given below which is written in Fortran 77.Alternatively a Motorola 68000 microprocessor based system using aVERSAdos operating system for real time use is programmed with logicallyequivalent software.

The preferred software procedures for computing the weld quality anddetermining when to shut the welder off are shown in FIG. 3. Theprocedure involves an iterative loop whereby data is collected andprocessed continually as the weld is made. The iteration period is notcritical, though it should generally be less than 10% of the averageweld time so that the control logic may achieve moderately fine control.For alternatingcurrent welders, it is convenient to execute the loop athalf-cycles or full-cycle intervals. For directcurrent welders, theiteration period need not be synchronized to welder power.

The data acquisition function digitizes and stores the current andvoltage data. The waveform processing function computes the resistance,power and energy curves. The feature computation function searches forthe start of melting and computes the percent energy after melting, thepercent R-drop and the expulsion energies. The quality assessment logiccomputes the quality discriminant and the edge discriminant. Theoptional control logic issues a shutoff command to the welder controllerwhen the quality discriminant function has gotten above the good-weldthreshold by a certain percentage.

Determining the Onset of Melting

Statistical analysis of many test welds has shown that the time at whichthe knee of the resistance curve occurs is highly significant. Thephysical interpretation of this identifying marker is that it generallycorresponds to the onset of melting.

The procedure for identifying the time that melting begins in a weld isbased upon a combination of the following three physical principles:

a. The average temperature θ of the weld increases as electrical power Pis put into the weld: ##EQU2## where m is the mass of the weld and k₁(θ) is the specific heat of the material being welded (joules/deg/gm).The mass of the weld is given approximately by:

    m=ρdA                                                  (2)

where ρ is the density (gm/cm³) of the material being welded and d and Aare the dimensions of the weld volume. A is taken to be the crosssectional area of the electrode tips and d is the thickness of thestackup.

b. Due to latent heat of fusion, the specific heat k₁ (θ), which isrelatively constant for low temperatures, increases rapidly between thesolidus and liquidus temperatures. This produces a rapid increase in theeffective thermal capacitance of the weld zone. Typical schematic plotsof effective thermal capacitance vs θ are shown in FIG. 4. Because thespatial profile of the temperature is not constant throughout the weldvolume, plots of the effective thermal capacitance as a function ofaverage temperature vary somewhat from weld to weld.

c. The electrical resistance R of the material increases approximatelylinearly as the weld temperature increases: ##EQU3## where k₂ (ohm·cm²/cm/deg) is the material's thermal coefficient of electricalconductivity and k₃ (cm/cm²) is the weld geometry constant which relatesthe stackup geometry and the intrinsic material resistance to form theaggregate resistance of the weld. The geometry constant k₃ for theresistance is given approximately by:

    k.sub.3 =d/A                                               (4)

The effects of electrode and interfacial contact resistance are notincluded; it is assumed that contact resistance is negligible during theperiod when this equation is applied.

Combining equations 1, 2, 3 and 4 yields an expression by which a terminversely proportional to the specific heat of the weld may be computedfrom the measurable parameters resistance and power. First equation 1and 2 are multiplied to obtain: ##EQU4## Note that the dθ's cancel inequation 5, implying that temperature does not need to be measuredexplicitly to extract information about the specific heat. ##EQU5##Next, the stackup property equations 2 and 4 for the weld mass andresistance geometry are substituted into equation 6 to yield: ##EQU6##Cancelling the distance d and dividing through by the power P gives theinverse specific heat in terms of the resistance rate and electricalpower: ##EQU7## The left hand portion of equation 8 is computed at eachhalf cycle during the weld to obtain a time history of inverse specificheat. (The inverse form is computed to maintain mathematical stabilityof the R/P ratio. P is always positive but R may be zero or negative.)For welds where the power setting is constant throughout the weld, thevalue of P may be taken to be constant, and the division by P is notrequired. In this case, processing is performed directly on the R curve.

When the specific heat begins to rise, the R/P curve dropscorrespondingly. The time that melting begins is detected by analyzingthe drop in the R/P curve. For the present weld monitoring algorithm, athreshold of 25% of the peak value of R/P was found empirically to givegood weld quality prediction. Thus melting is assumed to begin when theR/P curve drops from its peak during bulk heating to a value of 25% ofthat peak.

The specific values of ρ, A and k₂, and the value of k₁ at lowtemperatures, need not be known to detect the onset of melting. As longas ρ, A and k₂ do not vary significantly with respect to the variationin k₁ (θ), all that must be observed is a relative drop in the R/P curveindicating the transition in specific heat.

In the original R curve, FIG. 1, the commencement of melting is seen asa transition from the bulk heating rise to the melting plateau, and thispoint is referred to as the knee of the curve.

Given that the three physical phenomena above were the only ones whichimpacted the behavior of the resistance curve throughout the history ofa weld, a typical R curve would consist, as illustrated in FIG. 5a, onlyof a rise followed by a flattening after the start of melting. Thesearch for the melting time would then consist of establishing abulk-heating reference level for R/P shown in FIG. 5b during the firstseveral weld cycles and then looking for a drop to 25% of that level.

In fact, however, as illustrated in FIGS. 6a and 6B, several otherphenomena may occur which significantly modify the behavior of the R andR/P curves. Before melting starts, the effects of contact resistancebreakdown at the beginning of the weld generally overshadow the effectsof bulk heating, so R starts out negative. If the steel is galvanized,the melting and vaporization of zinc, first between the steel sheets andlater on between the electrodes and the sheets, superimposes"disturbances" on the R curve which appear as oscillations on the R/Pcurve. After melting starts, indentation and expulsion result in dropsin the R curve which cause R/P to go negative. The R curves may alsorise significantly after expulsion. Additionally, the cool times inwelds introduce discontinuities in the R and R/P curves, and noinformation on these curves is available during the cool times. Thesearch for the start of melting must contain logic to isolate the bulkheating and melting phenomenon from the effects of contact breakdown,zinc coating related oscillations, indentation, expulsion and cooltimes.

The present procedure for locating the start of melting consists ofthree major steps. First a search is performed on the R curve toidentify the resistance peak-after-melting. With some key exceptionsdiscussed below, this peak is generally the maximum point on the Rcurve. It occurs after the onset of melting but prior to any identationor expulsion. The purpose of locating this peak is to remove the effectsof indentation and expulsion from the R/P curve by placing an upperlimit on the search regions for the peak bulk heating rate and for thetime of melting. A global search is done throughout the R curve to findthe peak. For most welds, the maximum value of the R curve occursbetween the melting and indentation phases, and a simple peak detectionroutine is sufficient to locate the point. There are two importantwelding conditions, illustrated in FIGS. 7 and 8, which can generatepeaks in the R curve that are higher than the peak-after-melting, andthe peak detection algorithm must accommodate these phenomena:

1. In welds with low heat in the early half cycles (i.e., welds withupslope or low heat first pulses) the initial contact resistance may behigher than the peak-after-melting. See FIG. 7.

2. In some multi-pulse welds where a cool period begins when the weld islate into bulk heating but the peak-after-melting does not occur untilthe next pulse, the peak-after melting may not get as high as theresistance value at the end of the prior peak. See FIG. 8.

The procedure to locate the resistance peak consists generally of asearch through the R curve for the absolute maximum value of R.Additionally, the following checks are designed into the peak detectionalgorithm to reject the location of resistance maxima resulting from thephenomena described above.

1. To prevent the false detection of contact breakdown peaks, the peaksearch routine skips the initial points on the R curve if the curvestarts out moving downward. Only when the resistance rate first goespositive does the search begin.

2. If the maximum value of R occurs at the end of a pulse, and R isstill rising at the end of the pulse, it is assumed that thepeak-after-melting has not yet occurred. This peak is ignored, and,assuming there are additional heat pulses, a new search for another peakis initiated at the beginning of the next pulse. The search region iscontinually reduced as long as the maximum values occur at the end of aheating pulse.

The second major step of the procedure is establishing the peak bulkheating rate. The peak bulk heating rate is taken to be the localmaximum point on the R/P curve just prior to the peak in the R curve.This avoids a peak caused by zinc activity as shown in FIG. 6b.Specifically the search finds the global R/P peak between the beginningof the weld and the peak after melting. Next, the search proceedsbackward, beginning at the time of the peak-after-melting andterminating at the global peak, searching for a local peak which is morelikely then the global peak to represent the true bulk heating rate. Alocal peak is taken to be the peak bulk heating rate if (a) its value isat least a given percentage (50% is recommended) of the global peakvalue, and (b) there is a local minimum between the global and localpeaks which is less than a given percentage (80% is recommended) of thelocal peak value. The first local peak meeting this criteria is taken tobe the true peak bulk heating rate. If no local peak meets the abovecriteria, the global peak is taken to be the peak bulk heating rate.

The third major step is locating the onset of melting by searching theR/P curve, beginning at the time of the peak bulk heating rate, for thepoint where the curve drops to a specified percentage of the peak bulkheating rate. In practice a threshold of 25% of R/P max provides areliable knee indicator but that threshold value is not critical. Forexample, if 50% of R/P max is used, the time-of-knee changes only asmall amount.

The routine for identifying the time-of-knee or onset of melting issummarized in the flowchart of FIG. 9.

The Nugget/Sticker Model

A weld is predicted to be a nugget if it is observed to progresssufficiently far through its metallurgical growth by the time thatheating is terminated. Conversely, it is predicted to be a sticker ifinsufficient growth is observed. The model does not monitor thesolidification of the nugget after the heating period. The modeltherefore assumes implicitly that there is sufficient hold time for thenugget to complete the solidification process before the electrodepressure is released.

The degree of weld growth is defined by two features. The first feature,%E, is the percentage of the total weld energy that is put into the weldafter melting has begun.

The cumulative energy required to get the weld to the beginning ofmelting is defined to be the reference energy E_(M) for the weld. Theabsolute amount of energy required to get to the beginning of melting,or to get to the point of making a nugget, varies considerably as afunction of material type, stackup geometry, electrode tip condition,electrode force, and welder heat profiles; however, it has been foundempirically that a weld will generally be a nugget if the total energyE_(T) put into the weld exceeds the melting energy E_(M) by a givenpercentage. The following ratio feature is computed by dividing theenergy after melting by the total energy in the weld: ##EQU8## %E hasproven empirically to be a fairly robust feature in that it variesdirectly with weld quality, but its value is influenced little byvariations in conditions such as material, stackup thickness, tipcondition, force, and heat profiles.

The %E feature has the added advantage that it is unitless.Miscalibrations in the voltage or current sensors will not effect thefeature values because the calibration constants in the numerator anddenominator cancel. The %E feature alone can be the basis of weldquality assessment, however, the accuracy of the model can be improvedby incorporating a second feature.

The second feature, %R_(drop), is the percentage drop of the peak of theR curve relative to R peak. Empirical evidence shows a small butsignificant set of nugget welds which do no exceed the %E threshold butwhich do show some evidence of indentation in the R curve. This evidenceof indentation is an indication that the weld is actually further alongin its growth than indicated by the %E feature alone.

A gradual drop in the R curve after the bulk heating rise is generallyinterpreted as indentation of the welder electrodes into the metal. Asthe electrodes indent and the distance across the sheets reduces, thereis less material impeding current flow, and the resistance drops.Computation of the %R_(drop) feature first involves the location of theresistance peak after the bulk heating rise. The resistance differentialbetween the peak and the lowest point on the R curve subsequent to thepeak is the R_(drop). The normalized %R_(drop) feature is the ratio ofthe drop to the peak value: ##EQU9## As is the %E feature, %R_(drop) isunitless, and its value does not depend on precise sensor calibration.Here the multiplier 100 for computing percentage has been omitted in the%E and %R definitions but are accounted for effectively in the modelcoefficients given below.

The above definition is adequate for single pulse welds. In multipulsewelds, however, there are generally significant drops in the resistanceduring the cool times. Because these drops are not attributable toindentation, the R_(drop) routine contains logic to ignore drops due tointerpulse cooling.

FIG. 10 illustrates resistance drop during the cool time. In thisexample, the resistance peak-after-melting occurs in the first heatpulse. Some drop designated A in the figure, occurs during the firstpulse and presumably results from indentation. The drop B, however,results primarily from cooling of the metal, although there may in factbe some continued indentation during the cool time.

After repeated bulk heating in the second pulse, a new local peak LP isachieved and the drop C is evidence of additional indentation. The%R_(drop) feature is taken to be the sum of A plus C divided byR_(peak).

The percent R_(drop) routine takes as its inputs the position and valueof R_(peak). Separate resistance drops are then computed for each heatpulse beginning with the one containing the peak-after-melting. For thepulse containing the peak, the R_(drop) is taken to be the differencebetween the peak value and the lowest point on the R curve subsequent tothe peak but within the pulse.

For each subsequent heating pulse, a search is performed to find themaximum resistance within the peak. The R_(drop) for that pulse is takento be the difference between the peak and the lowest value of R withinthe pulse after the peak.

The total %R_(drop) for the weld is the sum of the individual dropsdivided by the peak after melting: ##EQU10##

A discriminant metric y is defined to be a weighted sum of the energyand R_(drop) features:

    y=A.sub.o +A.sub.1 %E+A.sub.2 %R.sub.drop

A_(o) is a constant, A₁ and A₂ are the model coefficients and arederived empirically from the test data. The model output y is unitless.Useful coefficients for successful weld prediction have been determinedto be A_(o) =-0.53, A₁ =1 and A₂ =7.5. If y is greater than zero, it ispredicted that there is sufficient growth of the weld to call it anugget. Conversely, negative values of y imply a sticker.

The model coefficients A₁ and A₂ represent the amounts of energy orR_(drop) that must be achieved by a weld to be called a nugget.Mathematically, either the energy or R_(drop) may be sufficient byitself to justify a nugget call, but in practice there is never anyR_(drop) without some %E. A combination of energy and R_(drop) may bysufficient for a nugget call though the energy may not be adequate byitself.

The routine for executing the nugget/sticker model is summarized in theflowchart of FIG. 11.

Edge Detection

For this description constant power weld setting is assumed. Thus R isutilized rather than R/P. Of course the power normalization should beutilized where a variable power weld schedule is used. One geometricfeature of a weld that may be inferred by observation of the R curve isthe location of the electrode tips with respect to the edge of one ofthe metal sheets being welded. FIG. 12 illustrates three interior vs.edge conditions: (a) an interior condition, where the electrode tips arewell inboard of the metal edge, (b) a zero overlap edge condition whereone of the tips is fully on the sheet but the edge of the tip is at theedge of the sheet, and (c) a high overlap edge condition where theelectrode overlaps the edge of the sheet by approximately 50%.

The procedure presented here to discriminate between edge and interiorwelds is based upon the observation that the two types of welds expeldifferently. When (and if) interior welds expel, they generally do sowell after melting begins (indicated by the knee of the R curve), andthey do so violently. Prior to expulsion, the pool of molten metal iscontained by the surrounding solid material. During this time, the Rcurve remains high even though there may be some small R drop due toelectrode tip indentation. When the surrounding solid can no longercontain the pool of molten metal, the weld expels. At this time, thepool squirts out within one or two half cycles causing a violentstep-like drop in the R curve.

By comparison to interior welds, edge welds expel more gently. When theelectrode overlaps the edge of one of the metal sheets, melting occursat this edge, and there is no solid metal at the edge to contain themolten metal. The molten metal escapes, i.e., expels, continuously as itmelts. The R curve therefore begins to drop as soon as the meltingbegins, and this drop is generally more continuous, long term, and moregradual than the instantaneous drops observed in interior welds.

Typical examples of R curves from interior welds are shown in FIGS. 13a,13b and 13c. The top trace FIG. 13a shows the raw resistance curve R(t).The second curve FIG. 13b is the first time derivative of R(t), theresistance rate R. The third trace FIG. 13c is the third derivative, theresistance inflection R.

FIGS. 14a, 14b and 14c show corresponding curves for edge welds.

In order to quantify the above edge phenomenon for purposes ofdiscriminating edge and interior conditions, four timing pointers aredefined:

(1) T_(knee) : The time that melting begins.

(2) T₁ : The time, after the resistance peak, where the resistance ratefirst drops below a threshold R_(thresh). This event is intended toindicate the beginning of expulsion, i.e., the escape of molten metal.The threshold is set sufficiently negative that small resistance dropsdue to plastic deformation of solid metal will not trigger the event,but it is high enough that molten metal extruding from low-heat edgewelds will trigger the event. (A threshold value of -0.83 microohms perhalf cycle is adequate for 60 Hz welders operating on steel with stackupthickness between 75 and 150 mils.)

(3) T₃ : The time, after T₁, where the resistance rate first rises backabove the rate threshold. This event is intended to indicate the end ofthe first expulsion. (Multiple expulsions may occur, particularly in themultiple stackups. Typically the first expulsion results from the edgegeometry and the later ones are interior expulsions between the fullyoverlapped sheets. To detect an edge geometry, it is necessary toisolate and evaluate the first expulsion). T₃ is not computed if T₁ doesnot exist. If T₁ exists, but the weld is terminated before theresistance rate rises back above the rate threshold, T₃ is taken tooccur at the end of the weld.

(4) T₂ : The time, between T₁ and T₃, where the resistance drop ratepeaks, i.e., is most negative. This event is the inflection point of theresistance drop, and it is intended to indicate when the expulsion rateof molten metal is maximum.

Edge weld expulsions last a relatively long time (T₁ to T₃) with respectto interior expulsions, and they "begin" relatively much earlier(T_(knee) to T₁) after the knee than do interior expulsions. Expressedanother way, edge welds are in the process of expelling a greaterpercentage of the melting period between the knee and the completion ofexpulsion than are interior welds. See FIGS. 13 and 14. This gives riseto a candidate time feature: ##EQU11##

The normalization resulting from the ratio in this time feature rendersit somewhat insensitive to the overall speed of the weld, but theexistence of cool times between pulses or varying heat rate between orwithin pulses could offset the feature. More fundamental than how muchtime is taken to progress from one event to the next is how much weldenergy is absorbed by the weld during this period. Thus differentialenergies are substituted for differential times to obtain the energyfeature: ##EQU12##

The degree of inflection, i.e., the third derivative of R at the time ofthe maximum drop rate, shows how "steplike" the expulsion is, so itgives an indication of how "violent" the resistance drop is. Theinflection feature is defined as the third derivative of the resistancecurve at the inflection point T₂. FIGS. 13c and 14c show the R curve forthe entire weld time, however the value of R is required only for timeT₂. It is computed by taking the second derivative of the R curve attime T₂. To render the feature independent of calibration scale factorson the voltage and current sensors, and to eliminate sensitivity todifferent rates of overall weld growth R is normalized by the maximumresistance rise rate R_(max) :

    x.sub.I =R/R.sub.max

Thus the inflection feature x_(I) has the units of inverse time squared.

A flowchart of the edge detection procedure is shown in FIG. 15. Thereare two stages in the decision process. First, if no inflection point isfound to exist after the peak in the R curve, the weld is calledinterior. An underlying assumption here is that the weld had at least50% of its energy after the knee. This assumption is well foundedbecause 50% energy after the knee is generally required to make anugget. Because edge welds generally begin expelling very soon after theknee, welds are called interior if they go to completion without anexpulsion inflection.

Second, given that an inflection point has occurred, the edge/interiordecision is based on a linear combination of the energy and inflectionfeatures:

    y=B.sub.0 +B.sub.1 X.sub.E +B.sub.2 X.sub.I

where B₀, B₁ and B₂ are coefficient values which determine the thresholdfor the energy and inflection features X_(E) and X₁. Values of B₀ =1, B₁=1/0.36 and B₂ =1/1.50 have been found empirically to be effective forwelding steel stackups with thicknesses between 75 and 150 mils.

If y is positive, the weld is called interior (i.e., good), and, ifnegative, the weld is called edge.

It will thus be seen that based upon the weld/nugget discrimination andthe edge detection method described herein, both of which rely on theidentification of the resistance curve knee, useful techniques aredisclosed for assessing and/or controlling weld quality with a highdegree of confidence. It will also be seen that apparatus is revealedfor detecting the resistance knee and carrying out the weld analysismethods using digital computers programmed according to the disclosedroutines.

The embodiments of the invention in which an exclusive property orprivilege is claimed are defined as follows:
 1. A method of predictingthe quality of a resistance spot weld comprising the steps of:measuringthe weld resistance and power, determining from the resistancecharacteristic and the electrical power the onset of melting, derivingfrom the measured power the total energy put into the weld and theenergy put into the weld after the onset of melting and assessing thedegree of weld growth by determining the ratio of energy put into theweld after the onset of melting to the total energy and comparing theratio to an empirical standard ratio representing a good weld wherebythe quality of the weld is predicted as good when the measured ratioequals or exceeds the standard ratio.
 2. A method of predicting thequality of a resistance spot weld comprising the steps of:measuring theweld resistance and power, determining from the resistancecharacteristic and the electrical power the onset of melting, derivingfrom the measured power the total energy put into the weld and theenergy put into the weld after the onset of melting, calculating theratio of energy put into the weld after the onset of melting to thetotal energy, searching the measured resistance value to find theresistance peak and the resistance drop following the peak, calculatingthe ratio of the resistance drop to the resistance peak, and assessingthe degree of weld growth by calculating a weighted sum of the energyratio and the resistance ratio wherein the sum is a measure of weldquality.
 3. A method of predicting the quality of a resistance spot weldcomprising the steps of:measuring the weld resistance and power,determining from the resistance characteristic and the electrical powerthe onset of melting, deriving from the measured power the total energyput into the weld and the energy put into the weld after the onset ofmelting, calculating %E, which is the ratio of energy put into the weldafter the onset of melting to the total cumulative energy, searching themeasured resistance value to find the resistance peak and the resistancedrop following the peak, calculating %R_(drop), which is the ratio ofthe resistance drop to the resistance peak, and determining the degreeof weld growth by the model Y=A₀ +A₁ %E+A₂ %R_(drop) where A₀, A₁ and A₂are empirically derived coefficients and Y is a weld quality predictor,wherein when Y is greater than zero the weld is predicted to be good. 4.A method of predicting the quality of a resistance spot weld comprisingthe steps of:measuring the weld resistance and power, determining fromthe resistance characteristic and the electrical power the onset ofmelting, deriving from the measured power the total energy put into theweld and the energy put into the weld after the onset of melting, anddetermining weld quality by calculating the amount of energy put intothe weld after the onset of melting as a function of the total weldenergy and comparing the calculated result to a specified valuerepresenting a good weld whereby the weld quality is predicted as goodwhen the calculated result equals or exceeds the specified value.
 5. Amethod of predicting the quality of a resistance spot weld made byapplying a plurality of weld current pulses separated by coolingperiods, comprising the steps of:measuring the weld resistance andpower, determining from the resistance and the power the onset ofmelting, deriving an energy parameter by calculating the amount ofenergy put into the weld after the onset of melting as a function of thetotal weld energy, searching the measured resistance value to find themaximum resistance peak and any local resistance peaks occurring duringsubsequent current pulses, determining the sum of the resistance dropswithin individual pulses following the said maximum and local peaks,deriving a resistance drop parameter by calculating the ratio of the sumof the resistance drops to the resistance peak, and determining weldquality by calculating a weighted sum of the energy parameter and theresistance drop parameter.
 6. A method of controlling the quality of aresistance spot weld comprising the steps of:applying weld current to aweld zone, measuring the weld resistance and power, determining from theresistance characteristic and the electrical power the onset of melting,deriving from the measured power the total energy put into the weld andthe energy put into the weld after the onset of melting, assessing thedegree of weld growth by determining the ratio of energy put into theweld after the onset of melting to the total energy and comparing theenergy ratio to an empirical standard ratio representing a good weldwhereby the quality of the weld is predicted as good when the measuredratio equals or exceeds the standard ratio, and terminating the weldcurrent when the energy ratio reaches a value sufficient to assure agood weld.
 7. A method of controlling the quality of a resistance spotweld comprising the steps of:applying weld current to a weld zone,measuring the weld resistance and power, determining from the resistancecharacteristic and the electrical power the onset of melting, derivingfrom the measured power the total energy put into the weld and theenergy put into the weld after the onset of melting, calculating %E,which is the ratio of energy put into the weld after the onset ofmelting to the total cumulative energy, searching the measuredresistance value to find the resistance peak and the resistance dropfollowing the peak, calculating %R_(drop), which is the ratio of theresistance drop to the resistance peak, determining the degree of weldgrowth by the model Y=A₀ +A₁ %E+A₂ %R_(drop) where A₀, A₁ and A₂ areempirically derived coefficients and Y is a weld quality predictor,wherein when Y is greater than zero the weld is predicted to be good,and terminating the weld current when the weld quality predictor Yreaches a determined value greater than zero, whereby it is assured thatsufficient energy is applied to produce a good weld.
 8. Weld monitoringapparatus for determining whether a resistance spot weld is good,comprising:means for acquiring data representing the weld resistance andpower curves; and digital computer means for storing the acquired data,said computer means being programmed to: (a) determine from theresistance characteristic and the electrical power the onset of melting,(b) derive from the measured power the total energy put into the weldand the energy put into the weld after the onset of melting, and (c)assess the degree of weld growth by determining the ratio of energy putinto the weld after the onset of melting to the total energy andcomparing the ratio to an empirical standard ratio representing a goodweld whereby the quality of the weld is predicted as good when themeasured ratio equals or exceeds the standard ratio.
 9. Weld monitoringapparatus for determining whether a resistance spot weld is good,comprising:means for acquiring data representing the weld resistance andpower curves; and digital computer means for storing the acquired data,said computer means being programmed to: (a) determine from theresistance characteristic and the electrical power the onset of melting,(b) derive from the measured power the total energy put into the weldand the energy put into the weld after the onset of melting, (c)calculate the ratio of energy put into the weld after the onset ofmelting to the total cumulative energy, (d) search the measuredresistance value to find the resistance peak and the resistance dropfollowing the peak, (e) calculate the ratio of the resistance drop tothe resistance peak, and (f) assess the degree of weld growth bycalculating a weighted sum of the energy ratio and the resistance ratiowherein the sum is a measure of weld quality.
 10. Weld monitoringapparatus for determining whether a resistance spot weld is good,comprising:means for acquiring data representing the weld resistance andpower curves, and digital computer means for storing the acquired data,said computer means being programmed to: (a) determine from theresistance characteristic and the electrical power the onset of melting,(b) derive from the measured power the total energy put into the weldand the energy put into the weld after the onset of melting, (c)calculate %E, which is the ratio of energy put into the weld after theonset of melting to the total cumulative energy, (d) search the measuredresistance value to find the resistance peak and the resistance dropfollowing the peak, (e) calculate %R_(drop), which is the ratio of theresistance drop to the resistance peak, and (f) determine the degree ofweld growth by the model Y=A₀ +A₁ %E+A₂ %R_(drop) where A₀, A₁ and A₂are empirically derived coefficients and Y is a weld quality predictor,wherein when Y is greater than zero the weld is predicted to be good.11. Resistance spot weld apparatus for controlling weld qualitycomprising:means for applying weld current to a weld zone, means foracquiring data representing the weld resistance and power curves, anddigital computer means for storing the acquired data, said computermeans being programmed to: (a) determine from the resistancecharacteristic and the electrical power the onset of melting, (b) derivefrom the measured power the total energy put into the weld and theenergy put into the weld after the onset of melting, (c) calculate theratio of energy put into the weld after the onset of melting to thetotal cumulative energy, (d) search the measured resistance value tofind the resistance peak and the resistance drop following the peak, (e)calculate the ratio of the resistance drop to the resistance peak, (f)assess the degree of weld growth by calculating a weighted sum of theenergy ratio and the resistance ratio wherein the sum is a measure ofweld quality, and (g) issue a signal to the weld current applying meansto terminate the weld current when the weighted sum reaches a determinedvalue assuring that a good weld has been made.
 12. Resistance spot weldapparatus for controlling weld quality, comprising:means for applyingweld current to a weld zone, means for acquiring data representing theweld resistance and power curves, and digital computer means for storingthe acquired data, said computer means being programmed to: (a)determine from the resistance characteristic and the electrical powerthe onset of melting, (b) derive from the measured power the totalenergy put into the weld and the energy put into the weld after theonset of melting, (c) calculate %E, which is the ratio of energy putinto the weld after the onset of melting to the total cumulative energy,(d) search the measured resistance value to find the resistance peak andthe resistance drop following the peak, (e) calculate %R_(drop), whichis the ratio of the resistance drop to the resistance peak, (f)determine the degree of weld growth by the model Y=A₀ +A₁ %E+A₂%R_(drop) where A₀, A₁ and A₂ are empirically derived coefficients and Yis a weld quality predictor, wherein when Y is greater than zero theweld is predicted to be good, and (g) issue a signal to the currentapplying means to terminate the weld current when the weld qualitypredictor Y reaches a determined value greater than zero, whereby it isassured that sufficient weld energy is applied to produce a good weld.